Lattice Type Research Articles

Effects of lattice structure on the electronic properties of helically symmetric nanotubes

In the last decades, nanotubes with varied compositions, underlying lattice structures, and symmetries have been proposed. In this work, we theoretically investigate nanotubes with similar compositions and symmetries but with different underlying lattice structures. Our aim is to understand how the underlying lattice structure of the nanotubes may affect their electronic properties. In order to do so, helically symmetric BCN nanotubes with graphene and graphenylene lattice structures were studied. In the considered structures, helical stripes of C atoms were incorporated into BN nanotubes with different helical angles. The geometric optimizations of the helical structures were carried out by using the Parametric Method 3 (PM3), whereas the electronic properties were calculated within the Green function formalism by using the Rubio–Sancho technique. Our results indicate that the stability of the two types of nanotube follows a similar pattern, with the energy per atom increasing as the fraction of C–N and C–B bonds increases. On the other hand, the type of lattice plays a critical role in the electronic properties. Although all considered helically symmetric nanotubes are semiconductors, different underlying lattice structures lead to distinct features. Graphene lattice nanotubes present a tunable band gap, whereas graphenylene lattice nanotubes present a nearly constant band gap for all helical angles. By focusing on the role of the underlying lattice structure, our work highlights how strain or stress, associated with each underlying lattice structure, may be tools to customize the properties of the nanotubes.

Improving the energy absorption capacity of bending-dominated additively manufactured polylactic acid (PLA) lattices

This study aims to investigate the energy absorption performance of three bending-dominated lattice structures including quad-diametral (QD), quad-diametral-line (QDL), and dodecahedron (DO)). Compression test specimens with these three lattice types were manufactured using the material extrusion additive manufacturing technique with PLA material. The specimens were manufactured with different sets of values of the print temperature, layer thickness, and line width to identify their effect on the energy absorption performance. Taguchi’s method was utilized for this purpose which revealed that the temperature is the most effective and its optimized value is 225 °C. It was also found that the energy absorption performance of the DO lattice is superior to that of QD and QDL lattices. In the following set of experiments, the print temperature was fixed to its optimized value (i.e. 225 °C), and another process parameter (i.e. print speed) along with layer thickness and line width were investigated among eight different groups of DO lattices. Numerical investigations were also performed and validated based on the experimental results. Parametric studies were also done for the DO lattice to improve its energy absorption performance by changing the strut diameters and introducing grading to the struts at each lattice cell.

MFSE-based two-scale concurrent topology optimization with connectable multiple micro materials

The concurrent design of different lattice material microstructures and their corresponding macro-scale distributions has great potential in achieving both lightweight and desired multiphysical performances. In such design problems, the lattice microstructures are usually separately optimized on the basis of the homogenization method, and the possibly poor connectivity between them is a key factor that severely hinders the fabrication and application of optimized two-scale structures. To handle the microstructure connectivity issue, this paper proposes a novel microstructure connectable strategy to bridge the gap between the two-scale and the full-scale model using the material-field series expansion (MFSE) method. Assuming different lattice material types in several pre-defined macro-scale regions, describe all types of microstructural topology with different portions of one material field function and update them simultaneously during the optimization process. Benefits from the material field definition with spatial correlation, the microstructures are well-connected without requiring additional constraints in the topology optimization model. The energy-based homogenization method is utilized for bridging the two-scale with different microstructures, while a decoupled sensitivities analysis for the microscale is employed to enhance the computation efficiency. Additionally, the proposed method significantly reduces the dimension of design variables, resulting in lower optimizer spending. The effectiveness and efficiency of the proposed method are demonstrated by several benchmark two-scale problems. Compared to density-based connectable methods, the proposed framework is easy to implement and reduces computational time by an order of magnitude in the 2D case.

Improved mechanical performance of quasi-cubic lattice metamaterials with asymmetric joints

In this paper, we propose a simple method for the modification of the unit cells in the lattice metamaterials that provides an improvement of their impact strength. The idea is based on the introduction of small mutual offsets of the interconnected struts inside the unit cells. In such way, the joints between the struts become asymmetric and the overall geometry of the unit cells can be defined as the quasi-cubic with the axis of chirality. Considering four types of cubic lattices with BCC, BCT, FCC and octahedron structures, we modified their geometry and investigated the influence of the offsets and the unit cell size on the overall performance in static and dynamic tests. From the experiments we found that the small offsets (less than the strut diameter) can allow to increase the impact strength of 3d-printed polymeric specimens in 1.5–3 times remaining almost the same density and static mechanical properties. Based on the numerical simulations, we show that the explanation of the observed phenomena can be related to the increase of plastic deformations and damage accumulation in the unit-cells with asymmetric joints leading to the transition from the quasi-brittle to the ductile type of fracture in tested specimens.

Experimental behavior of lintels for AAC masonry buildings: Comparison among different solutions

AbstractThe paper investigates the experimental behavior up to failure of different types of lintels for AAC masonry buildings. At first, precast highly‐reinforced AAC lintels, that are quite widespread on the European and Turkish market, were tested in flexure, by considering different reinforcement type and arrangement. The second analyzed solution is represented by RC lintels cast within three juxtaposed special AAC elements with U section, acting as formwork and final external finishing. Also in this case, the effect of reinforcement type (lattice girders, ordinary rebars, or a combination of them) and reinforcement amount on the bearing capacity and mode of failure was analyzed. The experimental results highlight that precast AAC lintels available on the market are very light and are characterized by high stiffness in bending; however, being usually over‐reinforced, their failure is quite brittle. On the contrary, RC lintels cast within U‐shaped AAC blocks (“combined AAC‐RC” specimens) are heavier but can be easily designed to have a ductile behavior, by simply following design Standard recommendations for ordinary RC elements.

Self-rotation-symmetry transformation for tuning anisotropy of single type lattice structures with minimal surfaces

There have been many works on the mechanical properties of hybrid structures based on triply periodic minimal surfaces (TPMSs) with multiple types. However, hybrid structures with a single type are neglected, which casts a shadow over searching the properties of a single structural element. Here we propose a self-rotation-symmetry transformation (SRST) method to numerically and experimentally show that isotropy and anisotropy can be realized on one TPMS type. With SRST, multiple substructures with the same type rotate with angle θ and then symmetrically combine to form a new unit. With the change of θ, the ratio maximum to minimum modulus (Max/Min) of the 2D SRST P type unit is from 1.02 to 2.03, and that of the 3D SRST P type unit is from 1.07 to 2.15. Also, the SRST method can effectively tune elastic modulus in a given direction. For example, the elastic modulus is tuned from about 200–300 MPa for the 2D P lattice. Interestingly, the elastic modulus and anisotropy are changed independently of the volume fraction, since the volume of each substructure does not change when rotated. This method provides the feasibility of designing targeted mechanical properties with a targeted volume fraction for applications in energy, aerospace, optics, and medical fields.

Hybrid Lattice Boltzmann Approach for Simulation of High-Speed Flows

A lattice Boltzmann approach utilizing hybrid lattices for accurate simulation of high-speed transonic (TS) flows is presented in this study. Single-layer lattice models, such as D3Q19, are computationally efficient with low numerical dissipation, but are limited to simulate weakly compressible flows within subsonic Mach regime. Multilayer lattice models, such as D3Q33, are capable of simulating thermal and high-speed compressible flows in TS Mach regime, but suffer from a higher numerical dissipation and higher computational cost. To take full advantages of these two types of lattices, a simulation domain is divided into two regions, high-subsonic (HS) flow regions to be solved by single-layer lattices and TS flow regions to be solved by multilayer lattices. The interface connecting the HS and TS flow regions are represented by double-sided surfels to realize smooth flow transition and ensure satisfaction of fundamental conservation laws. The hybrid lattice Boltzmann approach is stable and robust, and it allows multiple HS/TS flow regions with arbitrary shapes. Extensive validation studies demonstrate that the proposed approach is capable of obtaining accurate aerodynamic prediction of flows with a wide range of Mach numbers, and preserving the low numerical dissipation advantage of single-layer lattices in aeroacoustic computations.

Modeling Mesoporous 3D-Printed Lattice Electrodes for Energy Storage

3D printing could offer the versatility to design and manufacture energy storage devices on demand. The precision and material flexibility of 3D printing is ideal for integrating porous electrodes that can enhance electrochemical performance[1]. This work analyzes the electrical conductivity of 3D-printed mesoscale strut lattices at the 100 μm – 1 mm scale with 40 – 90 % volumetric porosity to develop optimal electrodes for energy storage devices. We use a graph-theory-based model[2] to compute the conductivity of multiple 3D lattice types with either solid conducting struts or struts coated with conductive material. These structures show 3 – 5X higher conductivity than random conductive foams that lack an internal periodic mesostructure[3]. Using microstereolithography, we 3D print samples with high-resolution struts (< 70 µm) that maintain their shape and achieve high conductivity after carbonization at 700 ˚C. By tuning the lattice architecture, we manipulate the tradeoff between conductivity, weight, and porosity, validating our simulations with experimental measurements. These results demonstrate that that body-centered cubic (BCC) strut lattices have optimal conductivity per weight compared with other lattice types. Implementing these 3D-printed conductive lattices as supercapacitor electrodes, we see that the lattice architecture impacts the gravimetric capacitance of the devices as well as the mechanical strength, with octet structures outperforming both cubic and BCC lattices. Electrochemical impedance spectroscopy (EIS) shows that 3D-printed electrodes with higher porosity exhibit higher gravimetric double layer capacitance and lower charge transfer resistance, making them ideal candidates for use in supercapacitor electrodes as free-standing 3D hosts for active materials. CV characterization of the electrodes also illustrates how our graph theory-based model for 3D lattices can predict the optimal structure for energy storage. This model can also serve to predict electrode performance and tailor design for integration of higher surface area nanoporous materials on these conductive 3D printed scaffolds. This allows us to guide the design of 3D printed electrodes to minimize charge transfer resistance and achieve an optimal balance between gravimetric and volumetric energy density for device applications.[1] J. Zhao, Y. Zhang, X. Zhao, R. Wang, J. Xie, C. Yang, J. Wang, Q. Zhang, L. Li, C. Lu, Y. Yao, Advanced Functional Materials 2019, 29, 1900809.[2] J. E. Huddy, M. S. Rahman, A. B. Hamlin, Y. Ye, W. J. Scheideler, Cell Reports Physical Science 2022, 3, 100786.[3] F. G. Cuevas, J. M. Montes, J. Cintas, P. Urban, J Porous Mater 2008, 16, 675. Figure showing (a) designed octet (blue), cubic (orange), and BCC (red) lattice types as well as (b) SEM images of their experimental 3D-printed counterparts and (c) measured electrical resistance. Figure 1

Distances in the face-centered cubic crystalline structure applying operational research.

The f.c.c. (face-centered cubic) grid is the structure of many crystals and minerals. It consists of four cubic lattices. It is supposed that there are two types of steps between two grid points. It is possible to step to one of the nearest neighbors of the same cubic lattice (type 1) or to step to one of the nearest neighbors of another cubic lattice (type 2). Steps belonging to the same type have the same length (weight). However, the two types have different lengths and thus may have different weights. This paper discusses the minimal path between any two points of the f.c.c. grid. The minimal paths are explicitly given, i.e. to obtain a minimal path one is required to perform only O(1) computations. The mathematical problem can be the model of different spreading phenomena in crystals having the f.c.c. structure.

Atomistic study of hydrogen diffusion in presence of defects in bcc and fcc iron

We present classical atomistic study of hydrogen diffusion in α-Fe and γ-Fe in presence of grain boundaries, surfaces or vacancies. Being pronounced traps for hydrogen, defects of different complexion play an important role in diffusion mechanisms related to hydrogen embrittlement. Clarification of hydrogen interaction with isolated defects is a necessary step towards establishing the hierarchy of related diffusion coefficients. We estimated possible impact of the above-mentioned defects on the H diffusion using recently developed interatomic potential capable of simulations of α and γ Fe phases. From the classical simulations we found that H interplay with defects may strongly depend on the host Fe structure: in fcc Fe, grain boundaries and surfaces provide accelerating path for diffusion, while in bcc we see no such effect. In case of a mono-vacancy, binding with hydrogen leads to reduction in a vacancy migration rate for both lattice types. However atomistic mechanisms of such slow-down are different. For bcc Fe we also estimated equilibrium hydrogen concentrations at grain boundaries and discuss a role of hydrogen located in GBs in overall hydrogen flux in polycrystal.

Modal analysis of a lattice type metamaterial by modeling cell structures using Euler–Bernoulli beams

Metamaterials have superior properties compared to materials found in nature and allow the tailoring of static and dynamic characteristics of the cell structures. In this study, the vibration characteristics of the sandwich plate systems composed of lattice beam structures are investigated and their behavior under various loading conditions is determined. In this context, a matrix-based solution method is developed to calculate the natural frequencies of the structure by assuming lattice elements as individual Euler–Bernoulli beams. The same structures are also analyzed with a commercial finite-element solver (ANSYS) to compare the results. In order to verify the results and determine the applicability of the proposed approach, an experimental study is conducted. Unit cell structures are additively manufactured with Stereolithography (SLA) and experimental modal analysis is performed using impact testing. Also, the amount of deflections on the structures under various loading conditions is determined experimentally by performing three-point bending tests on the plates. It has been concluded that approximate vibration characteristics of lattice-type metamaterial structures with various unit cell geometries can be determined in a short time by utilizing the matrix-based method without the need for any commercial software or performing complex experiments.

Tailorable thermoelasticity of cubic lattice-based cellular and granular materials by prestress

When a cubic lattice packaged by a boundary layer is subjected to a mechanical and temperature load, the force and length change of the bonds are equivalently evaluated by the average stress and strain of the unit cell. Provided a displacement gradient variation at a certain stress state, the variation of stress related to the strain variation provides the effective stiffness of the material at the corresponding configuration. It is discovered that the effective elasticity and thermal expansion coefficient can be tailored by the prestress through the boundary layer, which generates a configurational stress. Because the bonds of a cubic lattice depend on the material types, we consider the harmonic potential of springs for cellular lattices and Hertz's contact potential of balls for granular lattices, respectively. The cubic symmetry of effective elasticity is demonstrated for the three types of cubic lattices. By taking the orientational average, isotropic elastic constants can be obtained for randomly oriented lattices. As the bond length changes with the prestress of the boundary layer and controls the thermoelastic behavior, a novel design method of lattice-based materials confined in a spherical shell is demonstrated to achieve zero thermal expansion and a positive temperature derivative of elasticity.

Hybrid material usage in TPMS forms fabricated by additive manufacturing, comparison of mechanical strength of lattices produced with AlSi10Mg and 7050

Aluminum-based cellular structures are gaining significant attention across industries due to their lightweight and impressive mechanical properties. With the advent of additive manufacturing (AM), complex periodic cellular structures with varying unit cell forms, sizes, and volume fractions can be fabricated with relative ease. In this study, the mechanical strength of lattice structures fabricated using laser powder bed fusion (LPBF) was investigated, with a focus on the effect of lattice geometry, material type, and outer wall incorporation. Results showed that both material choice and lattice geometry significantly impacted the mechanical properties of the structures. The highest ultimate strength of 400 MPa was observed in the schwartz-p geometry model created with Al 7050 LPBF alloy, with the addition of Zr identified as the key factor in enhancing its strength. The incorporation of an outer wall did not improve the strength of the structures, indicating the importance of material and geometry selection in optimizing mechanical performance. These findings provide valuable insights for the development and advancement of lattice structures in various applications and highlight the potential of additive manufacturing in this field.

Analysis of crystal structure transition of polycrystalline 3C-SiC in nanocrystalline grinding based on molecular dynamics simulation

In order to study the grain/grain boundary crossing mechanism of polycrystalline 3C-SiC materials under nano-grinding, molecular dynamics(MD) method was used to simulate the grinding process of polycrystalline 3C-SiC materials under diamond abrasive particles. Through the coupling method of Voronoi construction of polycrystalline 3C-SiC workpiece model and MD construction process, the nano-grinding process of polycrystalline 3C-SiC material was established, the potential function field parameters were optimized, and the residual stress in polycrystalline 3C-SiC was eliminated. The energy transition equation is modified to reduce the time for the system to enter dynamic equilibrium. The crystal structure and dislocation generation of polycrystalline 3C-SiC were analyzed by post-processing methods such as defect analysis and crystal structure recognition. The results found that: there are cubic lattice, simple cubic lattice, hexagonal lattice and graphene mechanism type atoms at the grain boundary. During the machining process, the cubic lattice type atoms are converted to other types atoms, and other types structure atoms are converted to each other. The internal structure atoms of grains are converted to the grain boundary structure atoms during the machining process, and the crystal atoms near the grain boundary have low structural stability. The grinding force mainly acts on the forward direction and just below the grinding grain, and also has a small amount of distribution at the grain boundary, but it is relatively weak. The dislocation caused by grinding mainly occurs at grain boundaries. The resulting debris was monolithic, and a few were granular. The interconversion between grains and different structural atoms at the grain boundary is mainly from the crystal lattice atoms in grains to other atoms at the grain boundary. The force is transferred to the grain through the grain boundary, which hinders the transboundary transfer of force and protects the grains. The shearing force plays a dominant role in the grinding process.

Martensitic Transformation and the Electrical and Magnetic Properties of Ni51 – хMn36 + хSn13 (0 ≤ х ≤ 4) Alloys

The structures and electrical and magnetic properties of Ni–Mn–Sn-based alloys are studied.Changing the crystal lattice type in the course of martensitic transformation is found to be accompanied by substantial changes in the electrical resistivity. It is shown that for all the alloys under study negative magnetoresistanceis observed. The maximum magnetoresistance in a magnetic field of 18 kOe of ≈–45% was foundfor the Ni47Mn40Sn13 alloy.

Tri-granularity attribute reduction of three-way concept lattices

A real-world dataset often generates a huge concept lattice that may be difficult to understand and impractical to use. The principle of granular computing is that we can understand and use a complex whole at multiple levels of granularity. In light of this, we propose a unified tri-granularity model of various types of concept lattices, which allows us to examine a huge concept lattice at three levels of granularity (i.e., the elementary granularity, local granularity and global granularity). Attribute reduction plays a fundamental role in three-way concept analysis, it simplifies the expression of three-way concepts and thus contributes to a better perception of the knowledge in three-way concept lattices. The tri-granularity model suggests an opportunity to investigate the tri-granularity attribute reduction of three-way concept lattices. The existing research on attribute reduction works at the global granularity but pays little attention to the local granularity, or, even less, to the elementary granularity. Driven by these issues, we supply definitions and methods of local granularity and elementary granularity attribute reduction of three-way concept lattices. These newly proposed two levels of attribute reduction with the existing global granularity attribute reduction together provide a framework for the tri-granularity attribute reduction of three-way concept lattices. We further analyze the relationships among the three levels of attribute reduction. Moreover, the efficacy of our suggested approach is illustrated by an example via the trisections induced by three-way concepts. Finally, we design two tri-granularity attribute reduction algorithms whose effectiveness is further examined by numerical experiments.

Smoothing the Rough Edges: Evaluating Automatically Generated Multi-Lattice Transitions.

Additive manufacturing is advantageous for producing lightweight components while addressing complex design requirements. This capability has been bolstered by the introduction of unit lattice cells and the gradation of those cells. In cases where loading varies throughout a part, it may be beneficial to use multiple, distinct lattice cell types, resulting in multi-lattice structures. In such structures, abrupt transitions between unit cell topologies may cause stress concentrations, making the boundary between unit cell types a primary failure point. Thus, these regions require careful design to ensure the overall functionality of the part. Although computational design approaches have been proposed, smooth transition regions are still difficult to achieve, especially between lattices of drastically different topologies. This work demonstrates and assesses a method for using variational autoencoders to automate the creation of transitional lattice cells, examining the factors that contribute to smooth transitions. Through computational experimentation, it was found that the smoothness of transition regions was strongly predicted by how closely the endpoints were in the latent space, whereas the number of transition intervals was not a sole predictor.

Manipulating the supermodes in photonic molecules: prospects for all-optical switching and sensing

A specific photonic structure, a photonic molecule (PM), formed by several ordered resonance microcavities (photonic atoms) supporting high-quality “whispering gallery” eigenmodes (WGMs) is considered theoretically. All PM atoms are bound together by WGM electromagnetic fields and constitute collective supermodes (SMs) of the whole molecule. Usually, the composition of the SM spectrum in a particular PM is determined only by its topology (atomic lattice type, interatomic gap). We propose another way to control the spectral composition of supermodes by using bilateral (double-sided) optical pumping of a PM provided by a variable phase shift between the optical excitation channels. We show that multiatomic PMs made of silicon microcylinders demonstrate more than tenfold amplification/suppression of particular supermode intensity located in the Stokes/anti-Stokes wing of the molecular spectrum. This may be beneficial for the engineering of PM-based intensity-dependent sensors of refractive index changes in optical pumping buses or an all-optical thyristor with high switching range.

Preface to the special issue: Orthogonal polynomials and integrable systems, Peakons, Toda lattices and Painlevé transcendents

Since the 1990s, the theory of orthogonal polynomials has been increasingly playing an essential role in integrable systems, in particular Toda type lattices, peakon dynamical systems of Camassa–Holm (CH) type, as well as Random Matrix theory, and Painlevé Transcendents. This special issue focuses on recent advances in these areas. Still, in addition to research papers, it also includes review articles providing an overview of the pertinent developments which have impacted the synergy of the theory of integrable systems, approximation theory, and the theory of orthogonal polynomials and generalizations.

Sensitivity of the thermodynamics of two-dimensional systems towards the topological classes of their surfaces

Using Monte Carlo simulations we study the two-dimensional Ising model on closed manifolds of various topologies near the critical point of the planar bulk system. To this end we consider triangular, square, and hexagonal lattices. We find that the corresponding universal scaling functions of the magnetic susceptibility χ, as well as those of the specific heat C, differ for distinct Euler characteristics K of the manifold. In particular, for each lattice decoration the maxima of the scaling functions of χ grow as K increases. For the specific heat this relationship is inverted: e.g., for each lattice decoration the maxima of the scaling functions of C on the spherical surface (Euler characteristic K=2) is smaller than on the projective plane (K=1) which, in turn, is smaller than on the torus and on the Klein bottle (both with K=0). We find that if the aspect ratio of the lattices is conform to a square geometrical shape, the magnetic susceptibility scaling functions for different lattice types differ only by a non-universal amplitude.